Statistical method for analyzing the performance of oilfield equipment

ABSTRACT

A statistical methodology is disclosed to provide time-to-event estimates for oilfield equipment. A method according to the present invention extracts unbiased information from equipment performance data and considers parameters interactions without recourse to data thinning. The analysis explicitly accounts for items of equipment that are still operational at the time of analysis. A method according to the present invention may also be utilized to apply survival analysis to any oilfield equipment components where time-to-event information has been recorded. The method of the present invention allows comparative reckoning between different components present in the system comprising several or many individual components and allows analysis of these components either individually or simultaneously, i.e., in the presence of other components.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.11/461,911 filed Aug. 2, 2006, which is pending.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a statistical method whichprovides time-to-event estimates for oilfield equipment, and, moreparticularly a method which utilizes survival analysis techniques foranalyzing time-to-event data.

2. Description of the Prior Art

Currently oilfield tool (and equipment) performance prediction andanalysis is conducted in an ad hoc fashion with varying degrees ofsophistication and quality of interpretation. A major concern is that ofbias being introduced into the analysis and hence into the results,either through the exclusion of data or by assumptions about theperformance of equipment at the time of data sampling. At the time of ananalysis, the analyst has a population of capital intensive oilfieldequipment from which to draw data. Some of this equipment may havealready failed at the time of the data was extracted, while otherinstalled equipment is still fully operational and had not failed at thetime the data was extracted. This latter subset of the population hasbeen the subject of improper analysis in the past in two particulars:(i) complete exclusion of the data set; or (ii) the inaccurateassumption that, at the time the data was drawn, the equipment hadfailed.

Survival analysis is a statistical methodology and testing hypothesis oftime-to-event data that has, for example, been applied in the medicalfield to analyze time-to-death of a patient after surgery, the cessationof smoking, the reoccurrence of disease. For most statisticalapplications, models for probability distributions are usually describedin terms of:

-   -   Probability Density Function (pdf) f(t): a function whose        integral over a given range is equal to the probability of        taking a value in that range.    -   Distribution Function F(t) (cumulative density function): the        probability of the event occurring by time t.        For survival analysis, however, it is appropriate to work with        different functions characterizing the distribution:    -   Survival Function S(t): the probability of surviving at least to        time t [sometimes known as a reverse cumulative density        function: 1-F(t)].    -   Hazard Function h(t): the potential of failure in the next        instant given survival to time t.

An Explanatory Variable (EV) is a variable that may influence equipmentbehavior. In conventional product-limit analysis, the investigation of asingle EV requires partitioning of data set into subsets for each levelof the EV and analysis is then performed independently on each subset.This has the effect of thinning the data which may result in lessreliable statistics. In an investigation of two or more EVs, thisproblem is compounded. For example, if it is desired to predicate how anElectrical Submersible Pump (ESP) System would behave in a deviated well(true/false) and an openhole well (true/false), four data subsets existto examine independently. As the number of EVs in an analysis isincreased, there will be some subsets that are sparsely populated.

SUMMARY OF THE INVENTION

A rigorous statistical methodology has been developed to providetime-to-event (e.g., failure) estimates for of oilfield equipment. Thistechnique extracts unbiased information from equipment performance dataand can consider parameter interactions without recourse to datathinning. The analysis explicitly accounts for items of equipment thatare still operational at the time of the analysis, thus removing asignificant source of bias in the results.

When the collection of the data on the equipment to be analyzed is made,certain items of the equipment have yet to fail. To ensure that the fullpopulation of equipment and tools is fully considered without any biasentering into the analysis, a method in accordance with the presentinvention comprises the step of assigning a censoring flag (e.g.,0=failure, 1=censored) to the equipment, e.g., an ESP. This step ofassigning a censoring flag is a distinguishing feature of the presentinvention and permits the application of a tried and tested statisticalsurvival analysis to the data. For oilfield equipment, survival analysisis effectively the only reasonable, bias-free and consistent approach toa performance analysis.

The first stage of a method according to the present invention comprisesExploratory Data Analysis (EDA). This first stage comprises theutilization of both Cox Proportional Hazard (CPH) and Kaplan-Meier (KM)modeling approaches to allow the user to become acquainted with the dataand to recognize anomalies and outliers. The primary purpose of EDA isto obtain a reasonable initial model for the stepwise model selectionprocedure (Stage 2). This initial model is realized through theapplication of various statistical tests that identify significantExplanatory Variables (EVs) when considered singularly. The tests may,for example, be log-rank or Peto tests for KM and likelihood ratio test(LRT) for CPH. A process according to the present invention may furthercomprise the application of a CPH-related test to consider theassumption of proportional hazards used in the CPH model. EDA may alsoidentify potential candidates for later transformation and grouping.

The second step in a method according to the present invention comprisesStepwise Model Selection. In one embodiment, a stepwise model selectionis applied using the Akaike Information Criteria (AIC). All possiblecombinations of the EVs that were found to be significant in the EDAstage are the range of models examined in the stepwise search. Theinitial model is the most complex from this range, i.e., that whichincludes all of these EVs. A result of this second stage is a model thathas identified the significant parameters in combination as opposed onlyidentifying significant EVs individually.

The third step in a method according to the present invention is FactorCollapsing. In this step, the number of levels of a factor iseconomized, e.g. by using a backward elimination process using LRTs. Theprocess iteratively considers the candidate models formed by allpossible pair-wise joining of factor levels within the EVs in thecurrent model. The least significant amalgamation is accepted for thecurrent model of the next iteration. If all possible collapses havesignificant p-values, then the process is stopped.

The fourth step in a method in accordance with the present inventioncomprises the inclusion of interactions/other EVs. In this stage,consideration is given to model refinement by applying stepwise modelselection using AIC from the current model. The range of models isbounded by the most complex that includes the current EVs, theirpair-wise interactions and the excluded EVs, not just those identifiedin Stage 1. The inclusion of previously disqualified EVs allows theconfirmation that they are indeed not necessary. The inclusion ofpair-wise interaction parameters allows the capture of EV effects thatare not behaving in an additive way. In other words, interactions allowan EV to have a different influence on survival over the differentvalues provided by considering another EV.

The fifth step of a process according to the present invention is ModelChecking where the proportional hazard assumption of the final model istested. A global test is employed to see, if overall, the model violatesthis assumption. If it does, then proportional hazard assumption testsfor individual EVs can suggest which of them violate the assumption. Anysuch variable needs to be declared as a strata variable in a stratifiedCPH model. Here separate baseline functions are fitted for the levels ofeach violating EV.

A method according to the present invention may also be utilized toapply survival analysis to any oilfield equipment components wheretime-to-event information has been recorded. The method of the presentinvention allows comparative reckoning between different componentspresent in the system comprising several, or many, individualcomponents, and allows analysis of these components either individuallyor simultaneously (in the presence of other components).

A method of performing a survival analysis on the components of an itemof equipment comprises the step of representing the data on saidcomponents in a counting process formulation of a Cox Proportionalhazards model. A method of the present invention next comprises the stepof applying an extension of the Cox Proportional Hazard model to thedata, and in one embodiment, the extension which is applied is asdescribed in Lunn, M. and McNeil, D., “Applying Cox Regression toCompeting Risks,” Biometrics (June 1995) [hereafter “Lunn extension”]. Amethod according to the present invention next comprises the step ofperforming individual survival analysis on each of the identifiedcomponents by using the five-stage method described above. The finalstep of a method according to the present invention is to establish thetime-to-event estimate for each of the recorded components, either takenindividually or in the presence of the other components, such that anestimate of competing risks is obtained.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph that illustrates the Kaplan-Meier curves after Stage 1of the method of the present invention as being applied for theExplanatory Variable [EV] “FieldID” (the name of the EV denoting thehydrocarbon producing field and is a unique identifier) in a subjectdata set pertaining to an ESP System.

FIG. 2 is a graph that illustrates the Cox Proportional Hazard curvesfor the same “Field ID” data used in FIG. 1.

FIG. 3 is a graph that illustrates a summary of critical p-valuestatistics for all 57 primary Explanatory Variables in the test data setpertaining to the ESP System referenced with respect to FIG. 1 and wherethe index on the x-axis refers uniquely to each of the 57 EV'sconsidered in the study.

FIG. 4 is a graph that illustrates the final model of survival curvesfor each combination of the Explanatory Variables Motor Series (denotedas “motser” in the data set), Cable Bands (denoted as “cblbds” in thedata set) and Cable Manufacturer (denoted as “cabmanf” in the data set)for the test data set pertaining to the ESP System referenced withrespect to FIG. 1.

FIG. 5 is a graph that illustrates the Final model of FIG. 4 for MotorSeries “D/L/I”, Cable Manufacturer “C” and Cable Bands “0” with 95%confidence interval (bounds) incorporated either side of the expectedsurvival curve.

DESCRIPTION OF SPECIFIC EMBODIMENTS

It will be appreciated that the present invention may take many formsand embodiments. In the following description, some embodiments of theinvention are described and numerous details are set forth to provide anunderstanding of the present invention. Those skilled in the art willappreciate, however, that the present invention may be practiced withoutthose details and that numerous variations and modifications from thedescribed embodiments may be possible. The following description is thusintended to illustrate and not to limit the present invention.

A method in accordance with the present invention is described withrespect to an Electrical Submersible Pump (ESP) system comprising 117separate records for ESPs either currently or previously installed.Those skilled in the art will also appreciate that a method according tothe present invention is not limited in its application to ESP systems,but rather may be applied to numerous types of oilfield equipmentsystems where any specific time-to-event understanding is desirable fromboth an operational assurance and financial standpoint. This istypically the case for equipment in place for extended periods of time,like ESPs, valves, permanent gauges, etc.

A method in accordance with the present invention utilizes a standardstatistical software package. Several such packages are commerciallyavailable. In one embodiment, the R statistical software package isutilized in the method of the present invention.

I. DEFINITIONS

As used in this specification and in the appended claims:

1. The term “Explanatory Variable” (EV) means a variable that mayinfluence equipment behavior. An EV may be a “factor” which is acategorized variable such as the type of equipment or a “covariate”which is a numerical variable.

2. The term “parsimony” means “praiseworthy economy in use of means toan end; avoidance of excess.” The term “parsimonious” is used todescribe a model which has parsimony.

II. DESCRIPTION OF A METHOD OF SURVIVAL ANALYSIS FOR OILFIELD EQUIPMENTSYSTEMS

A method according to the present invention may be applied to a set ofdata, e.g. EVs, that has been compiled or collected on the equipment tobe analyzed. Since certain items of equipment had not yet failed at thetime of data collection, a method according to the present inventionassigns a censoring flag to each such item of equipment. For example,this censoring flag may equal “0” if the equipment has failed and “1” ifthe equipment is censored.

A basic data check is then undertaken to ensure compatibility in theanalysis and to prevent system software and algorithmic failure andcrash due, for example, to divisions by zero or an unrealizable numbersof permutations plus, spurious data, inconsistent data (i.e. characterswhere numerical values were expected, etc.). This basic data checkinvolves checking for and discarding any EVs that are factors with lowcounts and the threshold delineating low counts can be set and changedby the user. In one embodiment, if a level has three or less members,then it is tagged accordingly. Such variables do not contain contrastinginformation that would allow for a variable effect to be estimated, andtherefore, should be excluded from the analysis as separate levels;rather, they are gathered together into a new composite level terms“Other”.

The method of the present invention was applied to data collected from asystem of ESPs from fields in Ecuador, South America operated by asingle major operating company. This data was selected for demonstrationdue to its tractable size (small enough to enable testing and debugging)yet rich enough to demonstrate all the necessary concepts. Furthermorethe data was “good” i.e. no data-holes or quality issues. Each ESPinitially had 64 EVs associated with it. Table I below is a list of thefinal 57 EVs considered in the ESP analysis from the original 64 EVsassociated with each ESP. The 57 were identified from a preliminaryanalysis of the data where perfectly correlated EV's were removed e.g.sysmanf and cabmanf were exactly the same, EV's with only 1 level wereremoved and also EVs with simply too many low-count (<=3) unique levels(i.e. well names) would result in just one level called “Other”. For thesurvival analysis that was applied to an ESP system, the lower part ofTable I shows that eight EVs were removed from the main analysis for thereasons indicated in the preceding paragraph. Furthermore low-count dataentries were grouped together into a composite class called “other” andare used in the analysis. These are distinct from zero-count entries,which are marked by “N/A”, and are not used.

TABLE I Index Explanatory Variable Type Levels 1 Field ID Factor 7 2Well ID Factor 12  3 Event ID Covariate N/A 4 Application Factor 2 5Deviated Well Factor 2 (T/F) 6 Open Hole Factor 2 (T/F) 7 Casing IDFactor 3 8 Corrosion observed Factor 2 (T/F) 9 Scale build-up in wellFactor 2 (T/F) 10 Abrasion observed Factor 2 (T/F) 11 ApplicationEngineer Factor 6 12 Field Technician Factor 8 13 Spooler OperatorFactor 6 14 Rig Factor 9 15 Panel Type Factor 8 16 Panel ManufacturerFactor 2 17 Variable Speed Drive Factor 3 18 Depth of ESP Covariate N/A19 System Manufacturer Factor 2 20 Pump Manufacturer Factor 2 21 PumpSeries Factor 5 22 Pump Type Factor 10  23 Pump Stages Covariate N/A 24Number of Pumps Covariate N/A 25 Intake Manufacturer Factor 3 26 IntakeSerial Factor 4 27 Intake Type Factor 6 28 Protector Manufacturer Factor2 29 Protector Serial Factor 4 30 Protector Type Factor 11  31 Number ofProtectors Covariate N/A 32 Motor Manufacturer Factor 2 33 Motor SeriesFactor 5 34 Number of Motors Covariate N/A 35 Motor Horsepower CovariateN/A 36 Motor Voltage Covariate N/A 37 Motor Amperage Covariate N/A 38Pressure Instr. Manuf. Factor 2 39 Cable Manufacturer Factor 3 40 CableType Factor 6 41 Actreas Factor 7 42 Tubing ID Factor 4 43 Tubing TypeFactor 5 44 Motor Controller Type Factor 4 45 Wellhead ID Factor 8 46J-Box present Factor 2 (T/F) 47 Meter Lead Factor 5 48 Check Valvepresent Factor 2 (T/F) 49 Bleeder Valve present Factor 2 (T/F) 50 UMBpresent Factor 2 (T/F) 51 Adaptor present Factor 2 (T/F) 52 Y-Toolpresent Factor 2 (T/F) 53 Centralizer present Factor 2 (T/F) 54 CableProtector present Factor 2 (T/F) 55 Cable Band Factor 3 56 PhasingFactor 2 (T/F) 57 Grounded Factor 2 (T/F) Removed due to 58 Packerpresent Low count 59 Shroud Present Low count 60 TVSS installed Lowcount 61 Number of Intakes Related to EV #34 62 Number of pump sectionsRelated to EV #24 63 Operator ID Related to EV #11 64 Client ID 1 levelonly

The first stage of a method according to the present invention comprisesExploratory Data Analysis of each EV that was not excluded from theanalysis as a result of the basic data check. In this first stage, bothKM and CPH for all non-excluded EVs are generated and considered.

The resultant statistic of only one single EV (namely FieldID from theESP study) is illustrated for demonstrative purposes. The EV FieldID hadseven levels (i.e., there were seven separate producing fields). FIG. 1illustrates the statistical curves for the EV FieldID for the test ESPSystem, while FIG. 2 illustrates the CPH curves for the same data asused in FIG. 1. Table II below presents the summary statistics of the KManalysis for this variable. Table III presents the same FieldIDstatistical data as Table II using the CPH model instead of KM.

TABLE II KM summary statistics for explanatory variable FieldID forseven fields in the ESP System (117 records with 2 NAs). Kaplan- MeierMean se Median 0.95 0.95 FieldID n days days days LCL UCL 1 9 500 119.9427 382 — 2 20 423 74.3 368 211 — 3 20 375 133.1 138 105 262 4 9 21489.5 49 27 — 5 26 624 180.1 167 143 436 6 5 452 157.3 457 93 — 7 26 34244.6 293 249 509 Statistical tests: log-rank: p-value = 0.1600; Peto:p-value = 0.432. Key: se: standard error of the mean, LCL and UCL:lower- and upper-confidence limits of the median respectively (in days),n: number of counts. Note that “—” denotes that the upper bound isundefined for the data provided.

TABLE III CPH summary statistics for explanatory variable FieldID forseven fields in the ESP System (117 records with two NAs). CPH Mean seMedian 0.95 0.95 FieldID n days days days LCL UCL 1 115 783 133.6 498242 — 2 115 569 83.5 319 214 1775  3 115 264 23.5 161 98 318 4 115 22918.2 154 50 466 5 115 466 61.3 260 166 546 6 115 494 67.3 264 149 — 7115 511 70.8 293 211 649 Statistical tests: LRT: p-value = 0.1950; CPH =0.818. Key: refer to Table B.1.

In accordance with the method of the present invention, stage 1exploratory data analysis (such as described above for FieldID) isrepeated for each EV in the data set. The statistical threshold(p-values=0.05) is used to demarcate the significance of each EV. Anyparameter falling below the critical p-value threshold indicates thatthis parameter is most likely to have a significant impact onperformance. The higher a parameter is above this threshold, the lesslikely it is to have an impact on performance.

FIG. 3 illustrates a plot of the p-value for each EV in the data set forthe ESP system. Table IV below shows the seven primary EVs that wereidentified, namely those characterized by falling below the criticalthreshold p-value=0.05. An additional three EVs (with indexes 8, 52 and53) with marginal statistical significance were also identified. Whilethese do not show as much significance as those in the primary list,they may turn out to be significant when building models when involvingmore than one EV. Both the KM and CM approaches identified the same setof seven significant EVs.

TABLE IV List of seven significant explanatory variables for singleparameter analysis (no collapsing) for both KM and CPH models (found atthe end of Stage 1. These were identified by (mostly) falling below thecritical threshold of p-value = 0.05. CPHA = Cox's Proportional Hazardsassumption test. KM Log- CPH Index Explanatory Variable rank LRT CPHA 16Panel Man 0.0150 0.0188 0.8900 17 Variable SD 0.0150 0.0255 0.9830 33Motor Series 0.0000 0.0008 0.3960 39 Cable Man. 0.0002 0.0022 0.0472 40Cable Type 0.0025 0.0188 0.0305 55 Cable Band 0.0016 0.0037 0.0471 57Grounded 0.0107 0.0120 0.0397

In accordance with the present invention, a stepwise model selection isnow performed, which is an iterative procedure involving adding ordeleting an EV at each stage. The choice to add or delete is made byconsidering all of the AIC values of models formed by single variableaddition or deletion from the current model. Any models that have alower AIC value than the current one are deemed to be better. For eachiteration, the best model (i.e. the one with the lowest AIC) is chosento be the current model for the next iteration. If there are no modelsthat have a lower AIC than the current model, the procedure terminates.

Table V below demonstrates the stepwise procedure from the initial modelthat includes all seven significant EVs identified in Stage 1. The fulloutput of the AIC analysis (not shown) provides information at eachiteration regarding the AIC of all models formed by the deletion of anEV in the current model and by the addition of an EV not in the currentmodel. The subsequent iterations in Table V have smaller AIC scores(indicating better models). In the above example, the current model ateach step is formed by successive deletion of an EV and at no subsequentsteps are these EVs ever returned into the current model. As noted abovesome EVs identified as significant in Stage 1 will not be deemedsignificant when combined with other such EVs. A reasonable model ofdata for Stage 2, as summarized in Table V has now been identified.

TABLE V The stepwise modeling process using AIC. The initial modelcomprises the seven significant EVs identified in Stage 1. AIC is usedto identify a parsimonious model that only includes three of these EVs.Step Model Variables (per Table 1) AIC Initial 16, 17, 33, 39, 40, 55,57 685.98 1 16, 17, 33, 39, 55, 57 (removed #40) 678.09 2 16, 17, 33,55, 57 (removed #17) 676.18 3 33, 39, 55, 57 (removed #16) 674.75 4 33,39, 55 (removed #57) 673.44 Final 33 (=Motor Series) and 673.44 39(=Cable Manufacturer) and 55 (=Cable Bands)

The stepwise process of Stage 2 suggests that only the three EVsidentified in Table V are required in a CPH model to adequatelyrepresent the data.

A method according to the present invention further includes the stageof factor collapsing, which may, for example, be implemented using aniterative process that at each stage identifies the “best” two levels tocombine for any factor having three or more levels. Thus, at eachiteration, every possible model formed by pair-wise combinations of thecurrent factor levels are compared to the current model via a LRT. Foreach candidate model a non-significant p-value (greater than 0.05)indicates that there appears to be no significant difference between thetwo combined levels. The “best” of all candidate models is given by theleast significant p-value: i.e., the one with the largest p-value above0.05. The model that yields such value is then chosen for the currentmodel in the next iteration. When no pair-wise combinations yieldnon-significant p-values, no further collapsing is possible because allremaining levels are significantly different and the algorithmterminates.

The fourth step in a method in accordance with the present inventioncomprises the stage of inclusion of interactions/other EVs. In thisstage, consideration is given to model refinement by applying stepwisemodel selection using AIC from the current model. The range of models isbounded by the most complex that includes the current EVs, theirpair-wise interactions and the excluded EVs, not just those identifiedin Stage 1. The inclusion of previously disqualified EVs allows theconfirmation that they are indeed not necessary. The inclusion ofpair-wise interaction parameters allows the capture of EV effects thatare not behaving in an additive way. In other words, interactions allowan EV to have a different influence on survival over the differentvalues provided by considering another EV.

The fifth step of a process according to the present invention is ModelChecking where the proportional hazard assumption of the final model istested. A global test is employed to see, if overall, the model violatesthis assumption. If it does, then proportional hazard assumption testsfor individual EVs can suggest which of them violate the assumption. Anysuch variable needs to be declared as a strata variable in a stratifiedCPH model. Here separate baseline functions are fit for the levels ofeach violating EV. FIG. 4 illustrates the final model of survival curvesfor each combination of EVs Motor Series, Cable Bands and CableManufacturer for the test data set pertaining to the ESP systemreferenced in FIG. 1 while FIG. 5 illustrates the final model of FIG. 4for the specific Motor Series “D/L/I”, Cable Manufacturer “C” and CableBands “0”, with 95% confidence interval (bounds) incorporated eitherside of the expected survival curve.

III. DESCRIPTION OF A METHOD OF SURVIVAL ANALYSIS FOR COMPONENTS OFOILFIELD EQUIPMENT

A method according to the present invention may also be utilized toapply survival analysis to any oilfield equipment components wheretime-to-event information has been recorded. The method of the presentinvention allows comparative reckoning between different componentspresent in the system comprising several, or many, individualcomponents, and allows analysis of these components either individuallyor simultaneously (in the presence of other components).

A method of performing a survival analysis on the components of an itemof equipment comprises the step of representing the data on saidcomponents in a counting process formulation of a Cox model. In oneembodiment, the i-th component may be represented by a set ofobservations: s_(ij), t_(ij), δ_(ij), x_(ij), k_(i), j=1, . . . n_(i),where (s_(ij), t_(ij)] is an interval of risk, open on the left andclosed on the right, δ_(ij)=0 if the component has failed at time t, and1 if the component has not failed. x_(ij) is the explanatory variablevector over the interval and k, is the component type stratum variable.In the present method we will thus produce multiple observations of eachcomponent in an installation, and multiple observations of individualcomponents across installations. In the data used in the above-describedsystem survival analysis:

-   -   s_(ij)=daystart    -   t_(ij)=dayend    -   δ_(ij),=eqstatus    -   k_(i)=comppart    -   x_(ij)=remaining explanatory variables.

With the method of the present invention, it is not necessary to havecontiguous observations. Observations that are not contiguous may, forexample, occur when considering a data set specific to a geographicregion and a temporary component is utilized in an installationotherwise outside its valid operation range before returning to aninstallation within its normal operating region.

A method according to the present invention next comprises the step ofapplying an extension of the Cox Proportional Hazard model to the data,and as noted above, in one embodiment the extension that is applied isthe Lunn extension. The Lunn extention is utilized because a keyassumption in the CPH model is that observed survival or event times areindependent. However, when dealing with component data, observationsinvolving components in the same installation are naturally related andmultiple observations of an individual component through its reuse arealso clearly related.

A method according to the present invention next comprises the step ofperforming individual survival analysis on each of the identifiedcomponents by using the five-stage method described above. The finalstep of a method according to the present invention is to establish thetime-to-event estimate for each of the recorded components either takenindividually or in the presence of the other components such that anestimate of competing risks is obtained.

Table VI below illustrates the results of applying the method of thepresent invention to data obtained with respect to ESPs. Section A ofTable VI illustrates a model for system well failure. Section B of TableVI illustrates a model for component failure not considered individuallybut treated as a system well failure. Sections C-F of Table VI,illustrate time-to-failure estimates for the protector, motor, intakeand pump, respectively, of the ESP, but performed individually. SectionG of Table F illustrates analysis of the components in the presence ofone another which provides a competing-risks estimate.

TABLE VI Hazards 95% Conf. Int. Variable Coef se(coef) z p Ratio LowerUpper Model for All Components PuMoPr.abrasionTRUE 2.14 0.397 6.623.5e−11 8.510 4.516 16.039 G chkvalveTRUE 1.59 0.338 4.79 1.7e−06 4.9232.563 9.456 PuInMo.cntrlizrTRUE −1.53 0.382 −3.84 1.2e−04 0.216 0.0990.473 PuMo.npull 1.28 0.269 5.28 1.3e−07 3.593 2.235 5.777PuMoPr.panelmfgREDA −1.85 0.274 −7.20 6.2e−13 0.157 0.095 0.260Pr.scaleTRUE −2.40 1.050 −2.25 2.4e−02 0.091 0.011 0.735 Model for PumpabrasionTRUE 1.58 0.648 2.78 5.4e−03 4.833 1.593 14.669 F cntrlizrTRUE−1.09 0.545 −2.13 3.3e−02 0.335 0.122 0.916 mtcVOLTRON-113 1.27 0.4613.02 2.5e−03 3.562 1.563 8.118 npull 1.48 0.386 4.07 4.7e−05 4.383 2.1518.928 panelmfgUnknown 1.43 0.424 3.40 6.8e−04 4.175 1.831 9.521 Modelfor Intake/GS chkvalveTRUE 1.96 0.632 3.25 1.1e−03 7.131 2.183 23.294 EcntrlizrTRUE −2.32 1.069 −2.28 2.3e−02 0.098 0.013 0.722 Model for MotorabrasionTRUE 2.357 0.692 4.06 4.9e−05 10.554 3.384 32.915 D npull 0.8780.396 2.41 1.6e−02 2.406 1.178 4.913 panelmfgREDA −1.901 0.443 −4.262.1e−05 0.149 0.062 0.359 Model for Protector abrasionTRUE 2.83 0.7194.70 2.7e−06 17.008 5.212 55.505 C panelmfgREDA −1.58 0.561 −3.032.5e−03 0.205 0.074 0.572 scaleTRUE −2.12 1.044 −2.05 4.0e−02 0.1190.016 0.912 Model for system: component failure scaleTRUE −5.500 2.025−2.72 6.6e−03 0.004 0.000 0.216 B mtcVOLTRON-113 1.901 0.461 4.123.7e−05 6.694 2.714 16.526 cntrlizrTRUE −1.323 0.608 −2.18 2.9e−02 0.2660.081 0.877 panelmfgREDA −1.315 0.372 −3.53 4.1e−04 0.268 0.129 0.557motnumb 0.319 0.389 0.82 4.1e−01 1.376 0.642 2.946 scaleTRUE:motnumb2.464 0.968 2.55 1.1e−02 11.754 1.764 78.370 Model for system: wellfailure cablemanufUnknown Strata — — — — — — A corosion Strata — — — — —— fieldid −1.071 0.343 −4.81 1.5e−06 0.343 0.222 0.530 wellevtno −0.1170.890 −2.05 4.0e−02 0.890 0.796 0.995 cblbands4 0.531 1.701 2.12 3.4e−021.701 1.040 2.783 wellmotorCL-562+ −1.970 0.139 −4.36 1.3e−05 0.1390.058 0.338 WellmotorOthers −1.422 0.241 −2.81 5.0e−03 0.241 0.089 0.651

1. A method for predicting, based on a statistical analysis, a time-tooccurrence of an event for an oilfield equipment system comprising: (a)identifying Explanatory Variables with respect to the oilfield equipmentsystem; (b) generating a model using the Explanatory Variables; and (c)interpreting the model to obtain an estimate of the time-to occurrenceof the event.
 2. The method of claim 1, wherein generating a model usingthe Explanatory Variables comprises performing an exploratory dataanalysis to identify Exploratory Variables that are likely to contributeto an occurrence of the event.
 3. The method of claim 2, whereingenerating a model using the Explanatory Variables further comprisesusing stepwise model selection.
 4. The method of claim 3, whereingenerating a model using the Explanatory Variables further comprisesusing factor collapsing.
 5. The method of claim 4, wherein generating amodel using the Explanatory Variables further comprises: includinginteractions between pairs of the identified Explanatory Variables andincluding previously disqualified Explanatory Variables to the modelobtained by using factor collapsing.
 6. The method of claim 5, whereingenerating a model using the Explanatory Variables comprises checkingthe model.
 7. A method for obtaining a model, based on a statisticalanalysis that provides a time-to-occurrence estimate of an event for anoilfield equipment system for which data respecting ExplanatoryVariables associated with the equipment system has been recorded,comprising: (a) applying a censoring flag to the data obtained for anitem of equipment that has not failed; (b) checking for and discardingany of the Explanatory Variables that do not contain contrastinginformation; and (c) performing an exploratory data analysis through theapplication of statistical tests to identify which of the ExplanatoryVariables are likely to contribute significantly to an occurrence of theevent.
 8. The method of claim 7, wherein the event is a failure of theequipment system.
 9. The method of claim 7, wherein step (c) isperformed by utilizing a Kaplan-Meier model.
 10. The method of claim 7,wherein step (c) is performed by utilizing a Cox Proportional HazardModel.
 11. The method of claim 7, further comprising using stepwisemodel selection.
 12. The method of claim 11, wherein the using stepwisemodel selection comprises selecting a combination of the ExplanatoryVariables that is likely to contribute significantly to an occurrence ofthe event.
 13. The method of claim 12, wherein the using stepwise modelselection comprises examining all possible combinations of theExplanatory Variables that were identified in step (c) of claim
 7. 14.The method of claim 12, wherein the using stepwise model selectioncomprises using Akaike Information Criteria.
 15. The method of claim 11,further comprising using factor collapsing in which the number of levelsof a factor is economized to obtain the model that provides thetime-to-occurrance estimate.
 16. The method of claim 15, wherein usingfactor collapsing comprises using a backward elimination process usinglikelihood ratio tests.
 17. The method of claim 15, further comprisingincluding interactions between pairs of the identified ExplanatoryVariables and including previously disqualified Explanatory Variables tothe model obtained by using factor collapsing.
 18. The method of claim17, further comprising checking the model.
 19. A method of obtaining atime-to-occurrence estimate of an event, based on a statisticalanalysis, for components of an oilfield equipment system for which dataon the components has been obtained, comprising: a) representing thedata in a counting process formulation of a Cox Proportional Hazardsmodel; b) applying a Lunn Extension to the data of step (a); and c)establishing time-to-occurrence models for each individual component inthe presence of the other components so as to produce a risks model. 20.The method of claim 19, wherein the event relates to electricalsubmersible pumps and the components include a pump, an intake, a motorand a protector.
 21. A method of obtaining a time-to-occurrence estimateof an event, based on a statistical analysis, for components of anoilfield equipment system for which data on the components has beenobtained, comprising: a) representing the data in a counting processformulation of a Cox Proportional Hazards model; b) applying a LunnExtension to the data of step (a); and c) establishingtime-to-occurrence models for each individual component.
 22. The methodof claim 21, wherein the event relates to electrical submersible pumpsand the components include a pump, an intake, a motor, and a protector.23. The method of claim 1, wherein the event is a failure of theequipment system.